Question: Solve for $b$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $-67b+6 \leq 9b + 43$
Solution: $\begin{aligned}-67b+6 & \leq 9b + 43 \\\\ -67b&\leq 9b+37 &(\text{Subtract } 6 \text{ from both sides}) \\\\ -76b &\leq 37 &(\text{Subtract } 9b \text{ from both sides})\\\\ 76b&\geq -37&(\text{Multiply both sides by }-1)\\\\ b&\geq-\dfrac{37}{76}&(\text{Divide both sides by }76) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $b \geq -\dfrac{37}{76}$.